"In fact, what solipsism means, is quite correct, only it cannot be said, but shows itself"
(Tractacus Logico-Philosophicus, §5.62).

There is a considerable difference between the way that Ludwig Wittgenstein addresses the problem of solipsism in his Tractatus Logico-Philosophicus and in his Philosophical Investigations. Chiefly, the former makes allowances for its possible truth whereas the latter proves it to be logically impossible. The difference lies mainly in Wittgenstein's conception of a "private language" which exists for each individual, understood only by himself or herself and no-one else: it is in looking more closely at this idea (and summarily disproving it) that solipsism collapses in upon itself. But Wittgenstein's point of attack is less the problem itself than it is the assumptions and presuppositions that underlie it -- and once they are shown to be unsound, the problem becomes irrelevant.

In the Tractatus, Wittgenstein proposes that solipsism is legitimate by leading up to it with a series of postulations, each of which builds upon those prior to it. His starting point is defining the limitations of the world itself: "The limits of my language mean the limits of my world" (Tractatus, §5.6). It follows thence that since "logic fills the world", then "the limits of the world are also its limits"; and thus that one cannot say with absolute certainty that some things exist in the world and others do not, as to do so would be to "say what we cannot think", which is impossible (§5.61). It is this last postulation through which solipsism comes to light, even though Wittgenstein doesn't define it directly:

That the world is my world, shows itself in the fact that the limits of the language (the language which I understand) mean the limits of my world. (§5.62)

By this token, thinking someone else's world with a language that is not theirs is illogical: just as the limits of one's own world are defined by the limits of one's own language, the limits of other people's worlds are marked off by themselves and their language. They are their own world, just as "I am my world" (§5.63). This is carried on into metaphysics with the suggestion that "the subject does not belong to the world but it is a limit of the world" -- just as language is (§5.632).

In some ways, there can be no "thinking, presenting subject" at all -- for by examining the world around one, one must also examine oneself and in so doing come to the conclusion that since every single component part can be used as an object, perhaps the notion of "subject" is something else entirely (§5.631). A compromise of sorts can be reached by removing the subject from the physical world; and to show that the subject can be dealt with in this way, Wittgenstein uses the analogy of the eye and its field of vision. "[F]rom nothing in the field of sight can it be concluded that it is seen from an eye", exactly as it is impossible for anyone to find a "metaphysical subject" anywhere in the world (§5.633). In solipsism, "the I" (or the subject) "shrinks down to an extensionless point", one that without physical existence is in an important sense outside the world, like the eye serves in a field of vision -- and so "solipsism strictly carried out coincides with pure realism", making it the best way to deal with the external world. Thus Wittgenstein's position in the Tractatus is that "what solipsism means, is quite correct, only it cannot be said, but shows itself" through examples like that of the eye and field of vision (§5.62).

The viewpoint that Wittgenstein expresses in the Philosophical Investigations is quite different -- it is that solipsistic thinking is illogical, even absurd. This turnabout is mostly owing to a change in his thoughts on the possibility of private languages and their ramifications. That such a thing as a language unique to a single person can exist is an assumption made in the Tractatus -- it is implicit to the definition of "my world" as limited by "the language which I understand" (Tractatus, §5.62). In the Philosophical Investigations, the assumption is uncovered, exposed as false, and summarily jettisoned in favour of the idea that language has some sort of universality, and that definitions of words come about only though social interaction.

A private language is one that can be understood by one person only, for whom it exists and from whose private experience and sensations it is derived (Philosophical Investigations, §243). The first problem with such a language is the connection between the sensations or feelings themselves and the words that one uses to describe them. Wittgenstein says that this problem is the same as the one that asks, "how does a human being learn the meaning of the names of sensations?", with the sensation of pain provided as an example (§244). This connection places the naming of sensations on the same plane as the naming of anything else -- "the verbal expression of pain replaces crying and does not describe it"; they are not precisely synonymous (§244). Interpreting the sensations felt by others is a second sticking point; is it possible to learn about the pain felt by another only by observing their behaviour? "[I]t makes sense to say about other people that they doubt whether I am in pain; but not to say it about myself," says Wittgenstein -- in this way sensations can be considered private, since when one is in pain one knows it for certain, even though others might not be so certain (§246).

If sensation is a private thing, then, that can only be guessed at by others, then how can one know whether or not a given sensation that one experiences -- pain, say, or the colour red -- is the same as the experience that another person would give that same name? Rearranging words to acknowledge that one's "own sensation of red" (§273) (one's own impression of what it is) might be different from someone else's does little to solve this issue, but it would seem that there is something greater to hand:

[D]on't we at least mean something quite definite when we look at a colour and name our colour-impression? It is as if we detached the colour-impression from the object, like a membrane. (§276)

Perhaps, then, the sensation itself is less important than the name it is given; in this way colours can be somehow universal, regardless of whether two people gesturing at the sky and commenting about how blue it is are experiencing the same sensation as they look at it. Wittgenstein's hypothetical situation of the "beetle in a box" is along these same lines: here we are given the example of a group of people who each have something in a box, and whatever is inside the box is called a "beetle" -- no-one is permitted to see anyone else's "beetle", and thus each person's experience of the "beetle" is confined to his or her observation of what is inside his or her own box (§293).

The interesting thing about the beetles in boxes is that it doesn't matter whether any of them are the same, whether they are constant or always changing or even whether there is anything at all inside any given person's box. In Wittgenstein's language-games, such an ephemeral, uncertain thing has no place at all -- and this in turn means that one can treat the "beetle" as a constant, and thus eliminate it from consideration. Thus, "if we construe the grammar of the expression of sensation on the model of 'object and designation' the object drops out of consideration as irrelevant" (§293).

The fact that the "beetle" means the same thing to everyone involved in this particular situation, no matter that each person's sensation of what the "beetle" is might differ, demonstrates that in this case the word's meaning is derived solely from its use in a social context: it has no meaning in and of itself. But it doesn't have to -- just as a verbal expression of pain replaces the act of crying, the word "beetle" replaces the object without actually needing to describe or define it, and red or blue or yellow can be experienced by anyone regardless of whether the sensation of colour experienced by each is identical. In this way, the argument for private language is dissolved -- it cannot exist, since language itself is constructed from social interaction.

Here at last solipsism itself is also hopelessly undermined: how can anything that must be verified by double-checking it against a public language exist in private? Since private language has been demolished and replaced by necessity with a public language, created and maintained in a social context, this particular problem that surrounds solipsism itself contains the presupposition of its answer: if the very language that we use to ask the question of whether or not it is a legitimate possibility is formulated in public, then other minds must exist.

Wittgenstein, Ludwig. "Philosophical Investigations (Selections)", trans. G.E.M. Anscombe. Foundation Year Programme Handbook. Halifax: University of King's College, 2004-2005.
Wittgenstein, Ludwig. "Tractatus Logico-Philosophicus (Selections)". Foundation Year Programme Handbook. Halifax: University of King's College, 2004-2005.